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Flow rate of fluid at burst leakage in pipeline due over pressured

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Rizkyffq

Mechanical
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we have a project to how knowing the flow rate of fluid at the burst leakage due over pressured, probably to make it easier to understand i will attach some pictures of this mechanism.

Pipe_1_uvvo6f.png


Picture at above is simply mechanism of pipeline system that installed vertically, with fluid is mud and density of the fluid is approximation 1500 kg/m3. The pipeline system having dead end pipeline and fluids generated by particular pump. If at the end of the pipeline there is a hole/orifice/leak that covered by something and that thing will open by over pressured from fluid inside of pipeline. we intended to make the end of pipeline that having hole/orifice/leak will burst due over pressure in case to make a burst flow rate for our research.

So we design that thing covered hole/orifice/leak will broke with pressure impacted it approximation in 4000 psi, so pump will produced flow rate and makes pressure inside the pipe line until 4000 psi. If thing that covered hole/orifice/leak already broken then we close the valve so there is no flow rate produces by the pump to pipeline, in this state there is no additional fluid that distribute to pipeline.

Pipe_2_qc1aqa.png


And automatically fluid inside pipeline will burst out from the pipeline with 4000 psi and because there is no additional pressure cause valve already close and pump stoped to distributing fluid then it is slowly become hydrostatic state.

pressure_ensh14.jpg


it is simple if we calculate the flow rate in hydrostatic state because we just need to know height of fluid (head), but what we confusing now is to know how to calculate the initial flow rate when burst fluid started after covered hole/orifice/leak forced opened due over pressured from the inside (4000 psi).

is it right to use this equation to calculate the burst leakage flowrate ?
1212121212_gqi09w.png


and additional question :
1. When hole/orifice/leak forced opened due over pressured, is it true the pressure that in intial is 4000 psi will drop drastically in seconds towards zero (hydrostatic pressure) ? assume that outside of pipeline there is empty space so fluid that leakaged will freely flows out.
2. does Q1 = Q2 (continuity) will works in this mechanism when the first second of burst leakage happens ? so let say the Q1 is 5 litre/s from the pump then the Q2 that out from the hole is also 5 litre/s ?
 
Most of the initial flow will be due to the stored energy in the compressed fluid and expanded pipe.
 
You need to tell people that this sounds like a continuation of this thread...
~As I said before, you have a load of transient things going on here.

Your pipe will de-pressurize at the bottom from 4000 psi to about 2000 due to the hydrostatic head.

This is probably not a lot of volume but there are shock waves flying about so my guess is around 20 seconds before the column starts to act in steady state. But I don't think it's a calculation.

What is happening at what is basically an orifice is complex and whilst the maximum velocity at the orifice is sonic velocity (~1400m/ sec) it might start to exhibit choked flow at a lot less depending on liquid properties as it flashes across the orifice.

How long this hole will be at choked flow I don't know, but could be some time if the holes are small compared to the diameter of the tube.


Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
 
ok then, thanks for your reply sir, so basically there is will be "chocked flow" happens when the hole opened, then there is supersonic velocity will occurs in very short time. i think this is some enlightment but i have another question after i read your reply,

1. So is this same phenomenon with water hammer ? if same then may use this equation to knowing the super sonic velocity of the fluid ?

water_hammer_aexohw.png


where Ke is modulus bulk of fluid, i got this equation from
Capture_b7klep.png



2. if we want to prevent chocked flow that produced supersonic speed that makes flow rate burst out overly or probably minimize the supersonic speed of fluid that burst out from orifice ? is it right to prevent or minimize it to make nozzle over orifice/hole/leak ? cause i read some article that chocked happened because of shard edge of the hole ?
 
Is not choked flow only defined in compressible flow?

Ted
 
Where i read most of source saying that choked flow is works only in compressible fluid but i got this source


Critical_Flow_Rate_of_Bernoulli_yllp9y.png


is it valid to use this equation to predict how much flow rate at chocked state (burst leakage) for incompressible fluid (mud with density approximation 1500 kg/m3) ?
 
Liquids also exhibit the behavior of an increasing pressure drop across an orifice without further increase of flow rate. Liquids are compressible to some extent, although far less than gases and pressure change is transmitted in all fluids at sonic velocity, which causes discontinuity of pressure drop vs flow relation where sonic velocity is reached.
 
Choked flow in liquids is different to gas but does exist. You find it more in control valve discussions and technical data as it depends on how the liquid reacts under lower pressure as it goes through the restriction. If it starts to vapourise then you have choked flow.

Max flow is sonic velocity but could be a lot lower.

So I know it's an issue but you need to find a flow assurance engineer or suitable analysis program.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
 
What is the pressure outside the pipe at the time of bursting. Will it increase after the burst or is the released mud not affecting pressure outside the pipe?
 
The reference linked above is a study of supercritical fluid conditions.

The behaviour cannot be seen in incompressible flows, because tremendous pressure differences are necessary to reach sonic flow velocities through nozzles; therefore, one can say that in practice, choking flow phenomena do not exist in incompressible flows. As a result, decrease in back pressure always results in increase in mass flow rate as shown in Figure 1.2 [17].

Ted
 
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